The damage of core samples can occur during the cutting, tripping, and handling phases. The core damage must be prevented otherwise the properties would be adversely altered and thus the cores would not be representative. One of the most detrimental damages occurs during tripping when the core undergoes decompression and temperature drop from the bottomhole to the surface. This occurs when sufficient time is not allowed for the pore fluids in the center of the core to dissipate than in the annulus. As a result, excessive pore pressure differences and stresses are induced within the core body. This causes tensile failure manifesting as microfractures in its body. These adversely alter the core rock and mechanical properties. Therefore, the sample should be tripped slowly enough so that the induced pore pressure and stress difference do not become excessive and the core does not undergo tensile failure. On the other hand, this slow enough tripping rate should meet the operational rig costs so that it does not cause invisible lost time. Therefore, the optimal tripping speeds should be determined for each case. This should be used as the basis of selection for different methods. The industry has so far utilized only generic methods for selecting their core tripping speeds. Just recently, there has been some research which failed to consider the thermal effect, the mud cake effect, and mechanical properties, they did not either evaluate the induced stresses or the optimal rates. Therefore, in this work, a state-of-the-art thermoporoelastic model has been developed to find the optimal tripping rates, which also contributes to the candidate selection. This work includes 1) the modeling, derivation, and evaluation of the hydraulic and thermal effects including the neglected ones in the literature, i.e., the thermal, mechanical, and mud cake effects; 2) summing all the effects causing induced stresses; 3) checking the induced stresses with the failure criterion; 4) indicating if tensile failure occurs for a specified tripping rate. This process is repeated for different tripping rates until the optimal one is obtained. A standard procedure is proposed to determine the optimal tripping using a standard set of inputs and running the model. During the modeling process, the contributing parameters have been identified and their effects have been investigated. Among the parameters, the hydraulic diffusivity coefficient and the in-situ conditions have been detected and introduced as the main factors determining the optimal rates and the basis for coring candidate selection.